**Steps 1-2.**Same as the steps 1-2 in the algorithm described in chapter 2.**Step 3.**Computation of the multipole moments:In this step we use (3.53) and (3.54) [(3.83) and (3.84)] for the computation of the multipole moments associated with leaves. Also, we use (3.57) and (3.58) [(3.71) and (3.72)] for M2M translations tracing the tree structure of cells upward (decreasing ).

**Step 4.**Computation of the local expansion: In this step we use (3.60) and (3.61) [(3.74) and (3.75)] for M2L translations and (3.64) and (3.65) [(3.78) and (3.79)] for L2L translations tracing the tree structure of cells downward (increasing ).**Step 5.**Evaluation of the integral in (3.46): In this step we use (3.80)[(3.80)] for the direct computation and use (3.59) [(3.73)] for the evaluation of contributions with the local expansion.